Rincón was part of a combined no-hitter on July 12, 1997. After Francisco Córdova threw nine innings of no-hit ball, Rincón relieved him and pitched a scoreless 10th. Teammate Mark Smith then hit a three-run walk-off home run in the bottom of the 10th to give Rincón the win.[3] To date, it is the last no-hitter in Pirates history.

He throws a four-seam fastball, slider, changeup, and two-seam fastball. He is currently married to his wife Jaqueline, they have two children, a daughter, Damaris, and a son, Ricardo, Jr. He is mentioned multiple times in the movie Moneyball.